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2 May, 07:39

Ed bought $2,000 in stock shares one week before the stock price dropped $10.00. If he had waited for the price setback, he could have bought 10 more shares for the same amount. How many shares did he buy?

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  1. 2 May, 07:56
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    He bought 40 shares.

    Explanation:

    Step 1: Determine the initial stock price

    Use the expression below to determine the total initial stock price as shown;

    T=S*s

    where;

    T=total initial stock price

    S=initial stock price per share

    s=number of shares

    In our case;

    T=$2,000

    S=x

    s=unknown

    replacing;

    2,000=x*s

    s=2,000/x

    Step 2: Determine the final stock price

    Use the expression below;

    F=f*s2

    where;

    F=final stock price=$2,000

    f=final stock price per stock = (x-10)

    s2=final number of shares bought = (2,000/x) + 10

    replacing;

    2,000 = (x-10) { (2,000/x) + 10)

    2,000=x (2,000/x) + (10 x) - 10 (2,000/x) - 100

    (2,000=2,000+10 x-20,000/x-100) x

    2,000 x=2,000 x+10 x²-20,000-100 x

    2,000 x-2000 x=10 x²-100 x-20,000

    10 x²-100 x-20,000=0

    solving quadratically;

    x=[100±√{100² - (4*10*-20,000) }] / (2*10)

    x={100±√ (10,000+800,000) }/20

    x = (100±900) / 20

    x=1,000/20=50

    Initial stock price=$50

    Number of shares bought=2,000/x=2,000/50=40

    He bought 40 shares.
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